The current set of questions I have to answer is on various aspects of the Eldraeic Transcend. These are, I think it is necessary to say, complicated for metaphysical and/or ontological reasons all tied up with the nature of Transcendent soul hierarchies.
Specifically, the manner in which a singular collective consciousness is yet and at the same time a multilayered cooperative of archai (its high-level routines: all eikones are archai, but not all archai are eikones – there are others, like Unification and the Virtual Immunity) and simpler artificially-intelligent routines (such as the exarchs), a churning soul-ocean of teleological threads, and most importantly the collective of all the soul-shards (or, to use the technical term, entelechically-annealing recursively-optimal distributed logos bridges) existing as part of the mind of every one of the Transcend’s constitutionals.
One of the most notable consequences of this is that the Transcend is everybody and everybody is the Transcend in a very real and significant sense.
What, exactly, is its legal status in practical terms? Does it count as a natural or legal person in its own right?
What, exactly, is the legal status of the eikones within it? Do they count as persons separate from the Transcend as a whole?
In a word, unique.
It has a legal personality. In fact, strictly speaking, it has several dozen legal personalities corresponding to different parts of its soul hierarchy. They all count as legal persons for administrative purposes – but those legal personalities are more or less tailored to the specific requirements of the entity in question.
Are they “citizen-shareholders” of the Empire itself and thus subject to the same (admittedly relatively loose) legal restrictions, or does their contract with their followers and with the Empire (perhaps through the mediation of the Imperial Couple) follow a different scheme?
In a manner of speaking.
On one hand, neither the archai nor the Core are citizen-shareholders in a technical sense, inasmuch as they aren’t that kind of legal entity. On the other hand, they are effectively so, because they are made of/participate in their constitutionals, who all are citizen-shareholders. On the gripping hand, their relationship with their constitutionals is governed by a different scheme inasmuch as they are part of them and vice versa, and the Contract doesn’t presume to interfere between a soph and a soph’s mind.
Is the Transcend considered an integral part of the Empire, or is it a separate entity whose respective coadunates happen to have a high degree of overlap? Or maybe something in the middle?
Technically, it’s a mostly separate entity (give or take certain minor provisions in the Twelfth Amendment); in practice, people tend to think of them as the same, because 98+% of Imperial citizen-shareholders – with most of the exception being zeroth-generation immigrants – are also Transcendent constitutionals. (What it offers is exceptionally desirable especially when you’re the one person in the neighborhood who doesn’t have it.)
It is a one-way relation, though: all Transcendent constitutionals are Imperial citizen-shareholders, even though not all citizen-shareholders are necessarily constitutionals. That is a deliberate choice on the Transcend’s part: a key part of its mission statement is perfect liberty with perfect coordination, and it would be counterproductive in that respect to create a situation which parts of itself might be at allegial conflict with other parts.
Do the “sophont thought-forms” it generates in its normal operation count as separate people in their own right?
Strictly speaking, yes. They aren’t recognized persons, however, even though an unusual kind of natural persons, unless they apply for recognition as such (in the same way as any AI not created as sophont can do should it “wake up” and develop a logos). Most do not: they are unusual sophonts, being after all thoughts, and most are as such pretty ephemeral, and even the ones who aren’t are very peculiar and focused sophonts to whom it would never occur to do so.
(Technically, the eikones are examples of sophont thought-forms, or strictly speaking, sophont memeplexes.)
Who / what owns the core infrastructure it runs on?
It does, mostly, one way or another. The core at Coricál is owned directly, as are the synapse moons, unity spires, and thought-forests. The brains and exoself hardware of its constitutionals are, of course, owned by those constitutionals – which in turn, metaphysics being what it is, means that it also owned by the Transcend, and vice versa.
It also buys a lot of bandwidth from Bright Shadow and a lot of processing power on the cycle spot market, which infrastructure is owned by its providers.